# User contributions for Goodwine

From Bill Goodwine's Wiki

Jump to navigationJump to search

#### 7 August 2024

- 20:3020:30, 7 August 2024 diff hist +413 N P. 558, Eq. 11.87 Created page with "The equation should be <math> X_n(x) = c_4 \left[ -\frac{ \sin \sqrt{\lambda_n}L + \sinh \sqrt{\lambda_n}L }{ \cos \sqrt{\lambda_n}L +\cos \sqrt{\lambda_n}L } \left( \cos \sqrt{\lambda_n}x - \cosh \sqrt{\lambda_n}x \right) + \left( \sin \sqrt{\lambda_n}x - \sinh \sqrt{\lambda_n}x \right) \right] </math> Return to errata." current
- 20:2520:25, 7 August 2024 diff hist +86 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 11 current
- 20:2020:20, 7 August 2024 diff hist +1 P. 437, exercise 9.7 No edit summary current
- 20:1920:19, 7 August 2024 diff hist +246 N P. 437, exercise 9.7 Created page with "The second equation should be <math>X(s) = \frac{80}{\left( s^2 + 2 s + 4 \right) \left( s + 20 \right)} \left( \frac{1}{s} \right). /math> Return to errata."
- 20:1520:15, 7 August 2024 diff hist +190 N P. 626, Exercise 12.3, number 6 Created page with "The equation should be <math>\ddot x + x + x^3 = 0, x(0) = 1, \dot x(0) = 1</math>. Return to errata." current
- 20:1520:15, 7 August 2024 diff hist +95 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 12
- 20:0620:06, 7 August 2024 diff hist +450 N P. 417, line -9 Created page with "The equation should be: <math>\angle G(s) = \operatorname{tan}^{-1} \left( \frac{\operatorname{Im} k G(s)}{\operatorname{Re} k G(s)} \right) = \operatorname{tan}^{-1} \left( \frac{k \operatorname{Im} G(s)}{k \operatorname{Re} G(s)} \right) = \operatorname{tan}^{-1} \left( \frac{\operatorname{Im} G(s)}{\operatorname{Re} G(s)} \right), </math> Return to errata." current
- 20:0220:02, 7 August 2024 diff hist 0 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 9
- 19:5619:56, 7 August 2024 diff hist +325 N P. 404, lines 11 and 12 Created page with "<math> y_{ss} = A \sqrt{[Re(G(i \omega))]^2 + [Im(G(i \omega))]^2} \sin \left( \omega t + \phi \right)</math> and <math> y_{ss} = A \left| G \left( i \omega \right) \right| \sin \left( \omega t + \phi \right)</math> Return to errata." current
- 19:5319:53, 7 August 2024 diff hist +102 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 9
- 19:5119:51, 7 August 2024 diff hist +105 P. 359, peak time derivation No edit summary current
- 19:0019:00, 7 August 2024
diff hist
**+778** N P. 359, peak time derivation Created page with "The final result is correct, but there are multiple mistakes in the derivation of the peak time. The derivation should be: <math> \frac{d}{dt} y(t) = \zeta \omega_n e^{-\zeta \omega_n t} \left( \cos \omega_d t + \frac{\zeta}{\sqrt{1 - \zeta^2}} \sin \omega_d t \right) - e^{-\zeta \omega_n t} \left(- \omega_d \sin \omega_d t + \frac{\zeta \omega_d}{\sqrt{1 - \zeta^2}} \cos \omega_d t \right) </math> <math> \frac{d}{dt} y(t) = \zeta \omega_n e^{-\zeta \omega_n t} \left(..." - 18:5118:51, 7 August 2024 diff hist +53 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 9
- 18:4818:48, 7 August 2024 diff hist −25 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 4 Tag: Manual revert
- 18:4718:47, 7 August 2024 diff hist +25 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 4

#### 6 November 2023

- 14:0414:04, 6 November 2023 diff hist +8 P. 542, last boxed set of equations No edit summary current
- 14:0414:04, 6 November 2023 diff hist +60 P. 542, last boxed set of equations No edit summary
- 14:0314:03, 6 November 2023 diff hist +12 P. 542, last boxed set of equations No edit summary
- 14:0214:02, 6 November 2023
diff hist
**+595** P. 542, last boxed set of equations No edit summary - 14:0014:00, 6 November 2023 diff hist +253 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 11

#### 15 February 2023

- 21:1521:15, 15 February 2023 diff hist +355 Main Page →Papers current
- 21:0821:08, 15 February 2023 diff hist 0 Main Page →Papers
- 21:0321:03, 15 February 2023 diff hist +86 Main Page →Papers
- 21:0221:02, 15 February 2023 diff hist 0 Main Page →Papers
- 21:0221:02, 15 February 2023 diff hist 0 Main Page →Papers
- 21:0221:02, 15 February 2023 diff hist +219 Main Page →Papers
- 20:5320:53, 15 February 2023 diff hist +221 Main Page →Papers

#### 2 February 2023

- 20:1120:11, 2 February 2023 diff hist +1 Main Page →PhD Students
- 20:1120:11, 2 February 2023 diff hist +52 Main Page →PhD Students

#### 10 December 2021

- 21:2521:25, 10 December 2021 diff hist +59 Main Page →PhD Students
- 15:3715:37, 10 December 2021 diff hist +16 Main Page →PhD Students

#### 27 October 2021

- 18:1718:17, 27 October 2021 diff hist +17 Engineering Differential Equations: Theory and Applications, Springer 2010 No edit summary
- 18:1618:16, 27 October 2021 diff hist +6 Engineering Differential Equations: Theory and Applications, Springer 2010 →The One-Dimensional Wave Equation

#### 1 September 2021

- 17:3917:39, 1 September 2021 diff hist −11 Engineering Differential Equations: Theory and Applications, Springer 2010 →Bibliography
- 17:3817:38, 1 September 2021 diff hist +11 Engineering Differential Equations: Theory and Applications, Springer 2010 →Bibliography

#### 9 August 2021

- 14:3814:38, 9 August 2021 diff hist +280 N P. 590, line 16 Created page with "The expression <math>f\left(x(t) + c_2 f(x(t),t)\Delta t, t + c_4 \Delta t \right)</math> should be <math>f\left(x(t) + c_3 f(x(t),t)\Delta t, t + c_4 \Delta t \right)</math>..." current
- 14:3714:37, 9 August 2021 diff hist +1 P. 622, line 9 No edit summary current
- 14:3614:36, 9 August 2021 diff hist +65 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 12
- 14:2714:27, 9 August 2021 diff hist +102 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 11
- 14:2614:26, 9 August 2021 diff hist +68 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 11
- 14:2314:23, 9 August 2021 diff hist +60 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 11

#### 4 June 2021

- 14:5914:59, 4 June 2021
diff hist
**+503** N P. 206, lines 4 and 7 Created page with "The right expression on line 4 should be: <math>\hat \xi^1 = \left[ \begin{array}{c} \hat \xi_1^1 \\ \hat \xi^1_2 \end{array} \right] = \left[ \begin{array}{c} 1 \\ -i \end{a..." current - 14:5614:56, 4 June 2021 diff hist +87 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 6
- 14:5414:54, 4 June 2021 diff hist +287 N P. 205, lines -7 and -9 Created page with "Line -9 should be: <math>\xi(t) = c_1 \xi^1 e^{\lambda_1 t} + \cdots + c_n \xi^n e^{\lambda_n t}</math> and line -7 should be <math>\xi(t) = c_1 \xi^1 + \cdots + c_n \xi^n<..." current
- 14:5214:52, 4 June 2021 diff hist +150 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 6
- 14:4314:43, 4 June 2021 diff hist +271 Engineering Differential Equations: Theory and Applications, Springer 2010 →Chapter 9
- 14:3914:39, 4 June 2021 diff hist +186 N P. 209, line 9 Created page with "The line should be: Hence <math>\mu = 1</math> and <math>\omega = 2,</math> and Engineering Differential Equations: Theory and Applications, Springer 2010#Errata|Return t..." current
- 14:3814:38, 4 June 2021 diff hist +260 Engineering Differential Equations: Theory and Applications, Springer 2010 →Errata

#### 2 March 2021

- 16:3816:38, 2 March 2021 diff hist +78 Main Page →PhD Students

#### 14 October 2020

- 19:3619:36, 14 October 2020 diff hist +303 N P. 493, Fig. 11.4 Created page with "The magnitude of the curve for each mode is slightly too large. The plot incorrectly had coefficients of the modes of <math> \frac{9}{n^2 \pi 2} </math> instead of <math> \fra..." current